Clearly a concious decision has been made not to enable a queue for live chat support. But you do have a queue on the phone, which is of course very disruptive to the customer compared to simply waiting on live chat. It also discriminates against anyone uncomfortable making phone calls to strangers.
So, why is there no queue system for live chat? Why is it just "Messaging is currently unavailable. We apologise for any inconvenience caused." Don't apologise, it's insincere. Resolve the situation.
Just to head off the predictable canned response, this isn't "feedback", or a "feature request". It's an inquiry into why you don't have a facility in place to queue for live chat.
